Math Problem Statement
y=3x−2: Draw a graph of the equation on a coordinate plane. Label your axes, choose an appropriate scale, and plot at least three points.
Solution
import matplotlib.pyplot as plt import numpy as np
Define the function y = 3x - 2
def linear_function(x): return 3 * x - 2
Generate x values and calculate corresponding y values
x_values = np.linspace(-2, 3, 100) # Choose a range for x to cover more of the graph y_values = linear_function(x_values)
Plot the graph
plt.figure(figsize=(8, 6)) plt.plot(x_values, y_values, label="y = 3x - 2", color="blue")
Plot at least three specific points
specific_points_x = [-1, 0, 2] specific_points_y = [linear_function(x) for x in specific_points_x] plt.scatter(specific_points_x, specific_points_y, color="red")
Label these points
for (x, y) in zip(specific_points_x, specific_points_y): plt.text(x, y, f"({x},{y})", fontsize=9, ha='right')
Label axes and add title
plt.xlabel("x-axis") plt.ylabel("y-axis") plt.title("Graph of y = 3x - 2") plt.axhline(0, color='black',linewidth=0.5) plt.axvline(0, color='black',linewidth=0.5) plt.grid(True) plt.legend()
plt.show() <<ImageDisplayed>>successHere is the graph of the equation . The axes are labeled, and I’ve selected a scale to capture the line clearly. The graph includes three specific points: , , and , which are plotted and labeled on the coordinate plane.
Would you like additional details or have any questions?
Here are related questions for further exploration:
- How would the graph change if the slope were altered to 2 instead of 3?
- What would happen if we changed the y-intercept to 1 instead of -2?
- How can you determine the x-intercept of this line algebraically?
- How would you find the distance between two points on this line?
- What is the significance of the slope in real-world applications?
Tip: The slope, 3, indicates how steeply the line rises as x increases—specifically, for each unit increase in x, y increases by 3 units.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Coordinate Geometry
Slope-Intercept Form
Formulas
y = mx + b
Theorems
Slope-Intercept Form of a Line
Suitable Grade Level
Grades 6-8